0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : supatvars_int
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n136.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:30:08 CST 2018
1.33/1.54	% done 4638 iterations in 1.335s
1.33/1.54	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
1.33/1.54	% SZS output start Refutation
1.33/1.55	tff(cTHM261_pme, conjecture,
1.33/1.55	  (![P:(a > $o > $o)]:
1.33/1.55	     (((![Xx:a]:
1.33/1.55	          (?[Xp:(a > $o)]:
1.33/1.55	             ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
1.33/1.55	              P(Xp)))) & 
1.33/1.55	       (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
1.33/1.55	      ((![Xx:a,Xy:a,Xz:a]:
1.33/1.55	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
1.33/1.55	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
1.33/1.55	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
1.33/1.55	       (![Xx:a,Xy:a]:
1.33/1.55	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
1.33/1.55	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
1.33/1.55	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
1.33/1.55	tff(zf_stmt_0, negated_conjecture,
1.33/1.55	  (~
1.33/1.55	    (![P:(a > $o > $o)]:
1.33/1.55	       (((![Xx:a]:
1.33/1.55	            (?[Xp:(a > $o)]:
1.33/1.55	               ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
1.33/1.55	                P(Xp)))) & 
1.33/1.55	         (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
1.33/1.55	        ((![Xx:a,Xy:a,Xz:a]:
1.33/1.55	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
1.33/1.55	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
1.33/1.55	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
1.33/1.55	         (![Xx:a,Xy:a]:
1.33/1.55	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
1.33/1.55	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
1.33/1.55	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
1.33/1.55	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('1', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('2', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['1'])).
1.33/1.55	tff('3', plain,
1.33/1.55	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '2'])).
1.33/1.55	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('5', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['3', '4'])).
1.33/1.55	tff('6', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['5'])).
1.33/1.55	tff('7', plain,
1.33/1.55	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('8', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.33/1.55	    inference('sup-', [status(thm)], ['6', '7'])).
1.33/1.55	tff('9', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('simplify', [status(thm)], ['8'])).
1.33/1.55	tff('10', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('11', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['10'])).
1.33/1.55	tff('12', plain,
1.33/1.55	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '11'])).
1.33/1.55	tff('13', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['12', '4'])).
1.33/1.55	tff('14', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['13'])).
1.33/1.55	tff('15', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xx)),
1.33/1.55	    inference('clc', [status(thm)], ['9', '14'])).
1.33/1.55	tff('16', plain, ![X2 : a > $o]: (X2(sk_Xz1(X2)) | ~ sk_P(X2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('17', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true | ~ sk_P(X0) | ~ sk_P(X0) | X0 = sk_Xp(sk_Xz1(X0))),
1.33/1.55	    inference('sup-', [status(thm)], ['16', '7'])).
1.33/1.55	tff('18', plain, ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(X0)) | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['17'])).
1.33/1.55	tff('19', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a]: (X0(X1) = sk_Xp(sk_Xz1(X0), X1) | ~ sk_P(X0)),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['18'])).
1.33/1.55	tff('20', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a]:
1.33/1.55	      (~ X0(X1)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))
1.33/1.55	       | sk_Xp(sk_Xz1(X0)) = sk_Xp(X1)),
1.33/1.55	    inference('sup-', [status(thm)], ['19', '7'])).
1.33/1.55	tff('21', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a]:
1.33/1.55	      (~ X0(X1) | ~ sk_P(X0) | ~ $true | sk_Xp(sk_Xz1(X0)) = sk_Xp(X1)),
1.33/1.55	    inference('demod', [status(thm)], ['20', '4'])).
1.33/1.55	tff('22', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a]:
1.33/1.55	      (sk_Xp(sk_Xz1(X0)) = sk_Xp(X1) | ~ sk_P(X0) | ~ X0(X1)),
1.33/1.55	    inference('simplify', [status(thm)], ['21'])).
1.33/1.55	tff('23', plain,
1.33/1.55	    ![X0 : a]:
1.33/1.55	      (~ $true | ~ sk_P(sk_Xp(X0)) | sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0)),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '22'])).
1.33/1.55	tff('24', plain,
1.33/1.55	    ![X0 : a]: (~ $true | ~ $true | sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0)),
1.33/1.55	    inference('demod', [status(thm)], ['23', '4'])).
1.33/1.55	tff('25', plain, ![X0 : a]: sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0),
1.33/1.55	    inference('simplify', [status(thm)], ['24'])).
1.33/1.55	tff('26', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ sk_P(sk_Xp(sk_Xz1(X0)))),
1.33/1.55	    inference('sup+', [status(thm)], ['19', '16'])).
1.33/1.55	tff('27', plain,
1.33/1.55	    ![X0 : a > $o]: (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['26', '4'])).
1.33/1.55	tff('28', plain,
1.33/1.55	    ![X0 : a > $o]: (~ sk_P(X0) | X0(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
1.33/1.55	    inference('simplify', [status(thm)], ['27'])).
1.33/1.55	tff('29', plain,
1.33/1.55	    ![X0 : a]: (sk_Xp(X0, sk_Xz1(sk_Xp(X0))) | ~ sk_P(sk_Xp(X0))),
1.33/1.55	    inference('sup+', [status(thm)], ['25', '28'])).
1.33/1.55	tff('30', plain, ![X0 : a]: (sk_Xp(X0, sk_Xz1(sk_Xp(X0))) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['29', '4'])).
1.33/1.55	tff('31', plain, ![X0 : a]: sk_Xp(X0, sk_Xz1(sk_Xp(X0))),
1.33/1.55	    inference('simplify', [status(thm)], ['30'])).
1.33/1.55	tff('32', plain, (sk_Xp(sk_Xx, sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('sup+', [status(thm)], ['15', '31'])).
1.33/1.55	tff('33', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xx1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx))
1.33/1.55	     | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('sup-', [status(thm)], ['32', '7'])).
1.33/1.55	tff('34', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('demod', [status(thm)], ['33', '4'])).
1.33/1.55	tff('35', plain, (sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('simplify', [status(thm)], ['34'])).
1.33/1.55	tff('36', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('37', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['36'])).
1.33/1.55	tff('38', plain,
1.33/1.55	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '37'])).
1.33/1.55	tff('39', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['38', '4'])).
1.33/1.55	tff('40', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['39'])).
1.33/1.55	tff('41', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['40', '7'])).
1.33/1.55	tff('42', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('simplify', [status(thm)], ['41'])).
1.33/1.55	tff('43', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('clc', [status(thm)], ['42', '14'])).
1.33/1.55	tff('44', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('sup+', [status(thm)], ['43', '31'])).
1.33/1.55	tff('45', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xx1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xy))
1.33/1.55	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('sup-', [status(thm)], ['44', '7'])).
1.33/1.55	tff('46', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('demod', [status(thm)], ['45', '4'])).
1.33/1.55	tff('47', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('simplify', [status(thm)], ['46'])).
1.33/1.55	tff('48', plain,
1.33/1.55	    (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('sup+', [status(thm)], ['35', '47'])).
1.33/1.55	tff('49', plain, (sk_S2(sk_Xx1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['48'])).
1.33/1.55	tff('50', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
1.33/1.55	    inference('sup-', [status(thm)], ['28', '7'])).
1.33/1.55	tff('51', plain,
1.33/1.55	    ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['50'])).
1.33/1.55	tff('52', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a]:
1.33/1.55	      (X0(X1) = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), X1) | ~ sk_P(X0)),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['51'])).
1.33/1.55	tff('53', plain,
1.33/1.55	    ![X0 : a, X1 : a]:
1.33/1.55	      (sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1) | ~ sk_P(sk_Xp(X0))),
1.33/1.55	    inference('sup+', [status(thm)], ['25', '52'])).
1.33/1.55	tff('54', plain,
1.33/1.55	    ![X0 : a, X1 : a]:
1.33/1.55	      (sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['53', '4'])).
1.33/1.55	tff('55', plain,
1.33/1.55	    ![X0 : a, X1 : a]: sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1),
1.33/1.55	    inference('simplify', [status(thm)], ['54'])).
1.33/1.55	tff('56', plain,
1.33/1.55	    ![X0 : a]:
1.33/1.55	      (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xx)), X0) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('sup+', [status(thm)], ['49', '55'])).
1.33/1.55	tff('57', plain,
1.33/1.55	    ![X0 : a]: (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xx, X0) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('demod', [status(thm)], ['56', '55'])).
1.33/1.55	tff('58', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xy)
1.33/1.55	       | sk_S2(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('59', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['58'])).
1.33/1.55	tff('60', plain,
1.33/1.55	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '59'])).
1.33/1.55	tff('61', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['60', '4'])).
1.33/1.55	tff('62', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['61'])).
1.33/1.55	tff('63', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['62', '7'])).
1.33/1.55	tff('64', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('simplify', [status(thm)], ['63'])).
1.33/1.55	tff('65', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('66', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['65'])).
1.33/1.55	tff('67', plain,
1.33/1.55	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '66'])).
1.33/1.55	tff('68', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['67', '4'])).
1.33/1.55	tff('69', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['68'])).
1.33/1.55	tff('70', plain, (sk_S2(sk_Xx1) | sk_S1 = sk_Xp(sk_Xy)),
1.33/1.55	    inference('clc', [status(thm)], ['64', '69'])).
1.33/1.55	tff('71', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['70'])).
1.33/1.55	tff('72', plain,
1.33/1.55	    ![X0 : a]: (sk_S1(X0) = sk_Xp(sk_Xx, X0) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
1.33/1.55	    inference('sup+', [status(thm)], ['57', '71'])).
1.33/1.55	tff('73', plain, ![X0 : a]: (sk_S2(sk_Xx1) | sk_S1(X0) = sk_Xp(sk_Xx, X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['72'])).
1.33/1.55	tff('74', plain,
1.33/1.55	    ![X3 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ sk_P(X5)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('75', plain,
1.33/1.55	    ![X3 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | sk_S2(sk_Xx1)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ sk_P(X5)),
1.33/1.55	    inference('simplify', [status(thm)], ['74'])).
1.33/1.55	tff('76', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '75'])).
1.33/1.55	tff('77', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['76', '4'])).
1.33/1.55	tff('78', plain,
1.33/1.55	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['77'])).
1.33/1.55	tff('79', plain,
1.33/1.55	    (~ sk_S1(sk_Xz)
1.33/1.55	     | sk_S2(sk_Xx1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx))
1.33/1.55	     | ~ sk_Xp(sk_Xx, sk_Xx)
1.33/1.55	     | sk_S2(sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['73', '78'])).
1.33/1.55	tff('80', plain,
1.33/1.55	    (~ sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true | ~ $true | sk_S2(sk_Xx1)),
1.33/1.55	    inference('demod', [status(thm)], ['79', '4', '0'])).
1.33/1.55	tff('81', plain, (sk_S2(sk_Xx1) | ~ sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['80'])).
1.33/1.55	tff('82', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('83', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['82'])).
1.33/1.55	tff('84', plain,
1.33/1.55	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '83'])).
1.33/1.55	tff('85', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['84', '4'])).
1.33/1.55	tff('86', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['85'])).
1.33/1.55	tff('87', plain, sk_S2(sk_Xx1), inference('clc', [status(thm)], ['81', '86'])).
1.33/1.55	tff('88', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['87', '7'])).
1.33/1.55	tff('89', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['88'])).
1.33/1.55	tff('90', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['89'])).
1.33/1.55	tff('91', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xz)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('92', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['91'])).
1.33/1.55	tff('93', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S1(sk_Xz)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '92'])).
1.33/1.55	tff('94', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S1(sk_Xz)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['93', '4'])).
1.33/1.55	tff('95', plain,
1.33/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['94'])).
1.33/1.55	tff('96', plain,
1.33/1.55	    (~ sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_S2)
1.33/1.55	     | sk_S1(sk_Xz)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['90', '95'])).
1.33/1.55	tff('97', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('98', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['97'])).
1.33/1.55	tff('99', plain,
1.33/1.55	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '98'])).
1.33/1.55	tff('100', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['99', '4'])).
1.33/1.55	tff('101', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['100'])).
1.33/1.55	tff('102', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.33/1.55	    inference('sup-', [status(thm)], ['101', '7'])).
1.33/1.55	tff('103', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['102'])).
1.33/1.55	tff('104', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('105', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['104'])).
1.33/1.55	tff('106', plain,
1.33/1.55	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '105'])).
1.33/1.55	tff('107', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['106', '4'])).
1.33/1.55	tff('108', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['107'])).
1.33/1.55	tff('109', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xx)),
1.33/1.55	    inference('clc', [status(thm)], ['103', '108'])).
1.33/1.55	tff('110', plain, (sk_Xp(sk_Xx, sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['109', '31'])).
1.33/1.55	tff('111', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx))
1.33/1.55	     | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('sup-', [status(thm)], ['110', '7'])).
1.33/1.55	tff('112', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('demod', [status(thm)], ['111', '4'])).
1.33/1.55	tff('113', plain, (sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['112'])).
1.33/1.55	tff('114', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('115', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['114'])).
1.33/1.55	tff('116', plain,
1.33/1.55	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '115'])).
1.33/1.55	tff('117', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['116', '4'])).
1.33/1.55	tff('118', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['117'])).
1.33/1.55	tff('119', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['118', '7'])).
1.33/1.55	tff('120', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['119'])).
1.33/1.55	tff('121', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('clc', [status(thm)], ['120', '108'])).
1.33/1.55	tff('122', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['121', '31'])).
1.33/1.55	tff('123', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xy))
1.33/1.55	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('sup-', [status(thm)], ['122', '7'])).
1.33/1.55	tff('124', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
1.33/1.55	    inference('demod', [status(thm)], ['123', '4'])).
1.33/1.55	tff('125', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['124'])).
1.33/1.55	tff('126', plain,
1.33/1.55	    (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['113', '125'])).
1.33/1.55	tff('127', plain, (sk_S2(sk_Xy1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['126'])).
1.33/1.55	tff('128', plain,
1.33/1.55	    ![X0 : a]:
1.33/1.55	      (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xx)), X0) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['127', '55'])).
1.33/1.55	tff('129', plain,
1.33/1.55	    ![X0 : a]: (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xx, X0) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('demod', [status(thm)], ['128', '55'])).
1.33/1.55	tff('130', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xy1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('131', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['130'])).
1.33/1.55	tff('132', plain,
1.33/1.55	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '131'])).
1.33/1.55	tff('133', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['132', '4'])).
1.33/1.55	tff('134', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['133'])).
1.33/1.55	tff('135', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xz)),
1.33/1.55	    inference('sup-', [status(thm)], ['134', '7'])).
1.33/1.55	tff('136', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['135'])).
1.33/1.55	tff('137', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('138', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['137'])).
1.33/1.55	tff('139', plain,
1.33/1.55	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '138'])).
1.33/1.55	tff('140', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['139', '4'])).
1.33/1.55	tff('141', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['140'])).
1.33/1.55	tff('142', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xz)),
1.33/1.55	    inference('clc', [status(thm)], ['136', '141'])).
1.33/1.55	tff('143', plain, (sk_Xp(sk_Xz, sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['142', '31'])).
1.33/1.55	tff('144', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xz))
1.33/1.55	     | sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S1))),
1.33/1.55	    inference('sup-', [status(thm)], ['143', '7'])).
1.33/1.55	tff('145', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S1))),
1.33/1.55	    inference('demod', [status(thm)], ['144', '4'])).
1.33/1.55	tff('146', plain, (sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['145'])).
1.33/1.55	tff('147', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xy)
1.33/1.55	       | sk_S2(sk_Xy1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('148', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['147'])).
1.33/1.55	tff('149', plain,
1.33/1.55	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '148'])).
1.33/1.55	tff('150', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['149', '4'])).
1.33/1.55	tff('151', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['150'])).
1.33/1.55	tff('152', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['151', '7'])).
1.33/1.55	tff('153', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['152'])).
1.33/1.55	tff('154', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xy)),
1.33/1.55	    inference('clc', [status(thm)], ['153', '141'])).
1.33/1.55	tff('155', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['154', '31'])).
1.33/1.55	tff('156', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xy))
1.33/1.55	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S1))),
1.33/1.55	    inference('sup-', [status(thm)], ['155', '7'])).
1.33/1.55	tff('157', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S1))),
1.33/1.55	    inference('demod', [status(thm)], ['156', '4'])).
1.33/1.55	tff('158', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('simplify', [status(thm)], ['157'])).
1.33/1.55	tff('159', plain,
1.33/1.55	    (sk_Xp(sk_Xy) = sk_Xp(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['146', '158'])).
1.33/1.55	tff('160', plain, (sk_S2(sk_Xy1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['159'])).
1.33/1.55	tff('161', plain,
1.33/1.55	    ![X0 : a]:
1.33/1.55	      (sk_Xp(sk_Xz, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xy)), X0) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['160', '55'])).
1.33/1.55	tff('162', plain,
1.33/1.55	    ![X0 : a]: (sk_Xp(sk_Xz, X0) = sk_Xp(sk_Xy, X0) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('demod', [status(thm)], ['161', '55'])).
1.33/1.55	tff('163', plain, (sk_Xp(sk_Xy, sk_Xz) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['162', '0'])).
1.33/1.55	tff('164', plain, (sk_Xp(sk_Xx, sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup+', [status(thm)], ['129', '163'])).
1.33/1.55	tff('165', plain, (sk_S2(sk_Xy1) | sk_Xp(sk_Xx, sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['164'])).
1.33/1.55	tff('166', plain,
1.33/1.55	    ![X3 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ sk_P(X5)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xy1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('167', plain,
1.33/1.55	    ![X3 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | sk_S2(sk_Xy1)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ sk_P(X5)),
1.33/1.55	    inference('simplify', [status(thm)], ['166'])).
1.33/1.55	tff('168', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xy1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '167'])).
1.33/1.55	tff('169', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | sk_S2(sk_Xy1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['168', '4'])).
1.33/1.55	tff('170', plain,
1.33/1.55	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['169'])).
1.33/1.55	tff('171', plain,
1.33/1.55	    (~ $true
1.33/1.55	     | sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx))
1.33/1.55	     | ~ sk_Xp(sk_Xx, sk_Xx)
1.33/1.55	     | sk_S2(sk_Xy1)),
1.33/1.55	    inference('sup-', [status(thm)], ['165', '170'])).
1.33/1.55	tff('172', plain,
1.33/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ $true | ~ $true | sk_S2(sk_Xy1)),
1.33/1.55	    inference('demod', [status(thm)], ['171', '4', '0'])).
1.33/1.55	tff('173', plain, sk_S2(sk_Xy1),
1.33/1.55	    inference('simplify', [status(thm)], ['172'])).
1.33/1.55	tff('174', plain,
1.33/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S1(sk_Xz) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['96', '173', '4', '0'])).
1.33/1.55	tff('175', plain, (sk_S1(sk_Xz) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['174'])).
1.33/1.55	tff('176', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('177', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['176'])).
1.33/1.55	tff('178', plain,
1.33/1.55	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '177'])).
1.33/1.55	tff('179', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['178', '4'])).
1.33/1.55	tff('180', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['179'])).
1.33/1.55	tff('181', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('182', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['181'])).
1.33/1.55	tff('183', plain,
1.33/1.55	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '182'])).
1.33/1.55	tff('184', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['183', '4'])).
1.33/1.55	tff('185', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['184'])).
1.33/1.55	tff('186', plain,
1.33/1.55	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['185', '7'])).
1.33/1.55	tff('187', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['186'])).
1.33/1.55	tff('188', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('189', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['188'])).
1.33/1.55	tff('190', plain,
1.33/1.55	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '189'])).
1.33/1.55	tff('191', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['190', '4'])).
1.33/1.55	tff('192', plain, (sk_P(sk_S2) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['191'])).
1.33/1.55	tff('193', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('clc', [status(thm)], ['187', '192'])).
1.33/1.55	tff('194', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('195', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['194'])).
1.33/1.55	tff('196', plain,
1.33/1.55	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '195'])).
1.33/1.55	tff('197', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['196', '4'])).
1.33/1.55	tff('198', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['197'])).
1.33/1.55	tff('199', plain,
1.33/1.55	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['198', '7'])).
1.33/1.55	tff('200', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['199'])).
1.33/1.55	tff('201', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('202', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['201'])).
1.33/1.55	tff('203', plain,
1.33/1.55	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '202'])).
1.33/1.55	tff('204', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['203', '4'])).
1.33/1.55	tff('205', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['204'])).
1.33/1.55	tff('206', plain, (sk_P(sk_S2) | sk_S1 = sk_Xp(sk_Xy)),
1.33/1.55	    inference('clc', [status(thm)], ['200', '205'])).
1.33/1.55	tff('207', plain, (sk_S1 = sk_S | sk_P(sk_S2) | sk_P(sk_S2)),
1.33/1.55	    inference('sup+', [status(thm)], ['193', '206'])).
1.33/1.55	tff('208', plain, (sk_P(sk_S2) | sk_S1 = sk_S),
1.33/1.55	    inference('simplify', [status(thm)], ['207'])).
1.33/1.55	tff('209', plain, ![X1 : a]: (sk_S1(X1) = sk_S(X1) | sk_P(sk_S2)),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['208'])).
1.33/1.55	tff('210', plain, ($true = sk_S(sk_Xz) | sk_P(sk_S2) | sk_P(sk_S2)),
1.33/1.55	    inference('sup+', [status(thm)], ['180', '209'])).
1.33/1.55	tff('211', plain, (sk_P(sk_S2) | $true = sk_S(sk_Xz)),
1.33/1.55	    inference('simplify', [status(thm)], ['210'])).
1.33/1.55	tff('212', plain,
1.33/1.55	    ![X3 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ sk_P(X5)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | sk_P(sk_S2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('213', plain,
1.33/1.55	    ![X3 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | sk_P(sk_S2)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ sk_P(X5)),
1.33/1.55	    inference('simplify', [status(thm)], ['212'])).
1.33/1.55	tff('214', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | sk_P(sk_S2)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '213'])).
1.33/1.55	tff('215', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | sk_P(sk_S2)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['214', '4'])).
1.33/1.55	tff('216', plain,
1.33/1.55	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['215'])).
1.33/1.55	tff('217', plain,
1.33/1.55	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
1.33/1.55	    inference('sup-', [status(thm)], ['211', '216'])).
1.33/1.55	tff('218', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (sk_P(sk_S)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('219', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['218'])).
1.33/1.55	tff('220', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_P(sk_S)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '219'])).
1.33/1.55	tff('221', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_P(sk_S)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['220', '4'])).
1.33/1.55	tff('222', plain,
1.33/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
1.33/1.55	    inference('simplify', [status(thm)], ['221'])).
1.33/1.55	tff('223', plain,
1.33/1.55	    (~ sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_S2)
1.33/1.55	     | sk_P(sk_S)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['90', '222'])).
1.33/1.55	tff('224', plain, (~ $true | ~ sk_P(sk_S2) | sk_P(sk_S) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['223', '173', '4', '0'])).
1.33/1.55	tff('225', plain, (sk_P(sk_S) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['224'])).
1.33/1.55	tff('226', plain, sk_P(sk_S), inference('clc', [status(thm)], ['225', '192'])).
1.33/1.55	tff('227', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (sk_S(sk_Xx)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('228', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['227'])).
1.33/1.55	tff('229', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S(sk_Xx)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '228'])).
1.33/1.55	tff('230', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S(sk_Xx)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['229', '4'])).
1.33/1.55	tff('231', plain,
1.33/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['230'])).
1.33/1.55	tff('232', plain,
1.33/1.55	    (~ sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_S2)
1.33/1.55	     | sk_S(sk_Xx)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['90', '231'])).
1.33/1.55	tff('233', plain,
1.33/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S(sk_Xx) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['232', '173', '4', '0'])).
1.33/1.55	tff('234', plain, (sk_S(sk_Xx) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['233'])).
1.33/1.55	tff('235', plain,
1.33/1.55	    ![X3 : a > $o]:
1.33/1.55	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('236', plain,
1.33/1.55	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['235'])).
1.33/1.55	tff('237', plain,
1.33/1.55	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '236'])).
1.33/1.55	tff('238', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['237', '4'])).
1.33/1.55	tff('239', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
1.33/1.55	    inference('simplify', [status(thm)], ['238'])).
1.33/1.55	tff('240', plain, sk_S(sk_Xx),
1.33/1.55	    inference('clc', [status(thm)], ['234', '239'])).
1.33/1.55	tff('241', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.33/1.55	    inference('sup-', [status(thm)], ['240', '7'])).
1.33/1.55	tff('242', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
1.33/1.55	    inference('demod', [status(thm)], ['241', '226'])).
1.33/1.55	tff('243', plain, sk_S = sk_Xp(sk_Xx),
1.33/1.55	    inference('simplify', [status(thm)], ['242'])).
1.33/1.55	tff('244', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['243'])).
1.33/1.55	tff('245', plain, sk_S(sk_Xx) = $true,
1.33/1.55	    inference('sup+', [status(thm)], ['0', '244'])).
1.33/1.55	tff('246', plain, (~ $true | sk_P(sk_S2) | ~ $true | ~ $true | sk_P(sk_S2)),
1.33/1.55	    inference('demod', [status(thm)], ['217', '226', '245'])).
1.33/1.55	tff('247', plain, sk_P(sk_S2), inference('simplify', [status(thm)], ['246'])).
1.33/1.55	tff('248', plain, (sk_S1(sk_Xz) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['175', '247'])).
1.33/1.55	tff('249', plain, sk_S1(sk_Xz), inference('simplify', [status(thm)], ['248'])).
1.33/1.55	tff('250', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (sk_S(sk_Xy)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('251', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['250'])).
1.33/1.55	tff('252', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S(sk_Xy)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '251'])).
1.33/1.55	tff('253', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S(sk_Xy)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['252', '4'])).
1.33/1.55	tff('254', plain,
1.33/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['253'])).
1.33/1.55	tff('255', plain,
1.33/1.55	    (~ sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_S2)
1.33/1.55	     | sk_S(sk_Xy)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['90', '254'])).
1.33/1.55	tff('256', plain,
1.33/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S(sk_Xy) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['255', '173', '4', '0'])).
1.33/1.55	tff('257', plain, (sk_S(sk_Xy) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['256'])).
1.33/1.55	tff('258', plain, sk_S(sk_Xy),
1.33/1.55	    inference('clc', [status(thm)], ['257', '185'])).
1.33/1.55	tff('259', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('sup-', [status(thm)], ['258', '7'])).
1.33/1.55	tff('260', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
1.33/1.55	    inference('demod', [status(thm)], ['259', '226'])).
1.33/1.55	tff('261', plain, sk_S = sk_Xp(sk_Xy),
1.33/1.55	    inference('simplify', [status(thm)], ['260'])).
1.33/1.55	tff('262', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xz)),
1.33/1.55	    inference('sup-', [status(thm)], ['249', '7'])).
1.33/1.55	tff('263', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['262'])).
1.33/1.55	tff('264', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (sk_P(sk_S1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('265', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['264'])).
1.33/1.55	tff('266', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_P(sk_S1)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '265'])).
1.33/1.55	tff('267', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_P(sk_S1)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['266', '4'])).
1.33/1.55	tff('268', plain,
1.33/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
1.33/1.55	    inference('simplify', [status(thm)], ['267'])).
1.33/1.55	tff('269', plain,
1.33/1.55	    (~ sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_S2)
1.33/1.55	     | sk_P(sk_S1)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['90', '268'])).
1.33/1.55	tff('270', plain,
1.33/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_P(sk_S1) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['269', '173', '4', '0'])).
1.33/1.55	tff('271', plain, (sk_P(sk_S1) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['270'])).
1.33/1.55	tff('272', plain, (sk_P(sk_S1) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['271', '247'])).
1.33/1.55	tff('273', plain, sk_P(sk_S1), inference('simplify', [status(thm)], ['272'])).
1.33/1.55	tff('274', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['263', '273'])).
1.33/1.55	tff('275', plain, sk_S1 = sk_Xp(sk_Xz),
1.33/1.55	    inference('simplify', [status(thm)], ['274'])).
1.33/1.55	tff('276', plain, ![X1 : a]: sk_S1(X1) = sk_Xp(sk_Xz, X1),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['275'])).
1.33/1.55	tff('277', plain,
1.33/1.55	    ![X0 : a, X1 : a]:
1.33/1.55	      (~ sk_Xp(X1, X0)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xz1(sk_Xp(X1))))
1.33/1.55	       | sk_Xp(sk_Xz1(sk_Xp(X1))) = sk_Xp(X0)),
1.33/1.55	    inference('sup-', [status(thm)], ['55', '7'])).
1.33/1.55	tff('278', plain,
1.33/1.55	    ![X0 : a, X1 : a]: (~ sk_Xp(X1, X0) | ~ $true | sk_Xp(X1) = sk_Xp(X0)),
1.33/1.55	    inference('demod', [status(thm)], ['277', '25', '4', '25'])).
1.33/1.55	tff('279', plain,
1.33/1.55	    ![X0 : a, X1 : a]: (sk_Xp(X1) = sk_Xp(X0) | ~ sk_Xp(X1, X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['278'])).
1.33/1.55	tff('280', plain, ![X0 : a]: (~ sk_S1(X0) | sk_Xp(sk_Xz) = sk_Xp(X0)),
1.33/1.55	    inference('sup-', [status(thm)], ['276', '279'])).
1.33/1.55	tff('281', plain, ![X0 : a]: (~ sk_S1(X0) | sk_S1 = sk_Xp(X0)),
1.33/1.55	    inference('demod', [status(thm)], ['280', '275'])).
1.33/1.55	tff('282', plain, (sk_S1 = sk_S | ~ sk_S1(sk_Xy)),
1.33/1.55	    inference('sup+', [status(thm)], ['261', '281'])).
1.33/1.55	tff('283', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (sk_S1(sk_Xy)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('284', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['283'])).
1.33/1.55	tff('285', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S1(sk_Xy)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '284'])).
1.33/1.55	tff('286', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | sk_S1(sk_Xy)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xy1)
1.33/1.55	       | ~ X0(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['285', '4'])).
1.33/1.55	tff('287', plain,
1.33/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
1.33/1.55	    inference('simplify', [status(thm)], ['286'])).
1.33/1.55	tff('288', plain,
1.33/1.55	    (~ sk_S2(sk_Xy1)
1.33/1.55	     | ~ sk_P(sk_S2)
1.33/1.55	     | sk_S1(sk_Xy)
1.33/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['90', '287'])).
1.33/1.55	tff('289', plain,
1.33/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S1(sk_Xy) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['288', '173', '4', '0'])).
1.33/1.55	tff('290', plain, (sk_S1(sk_Xy) | ~ sk_P(sk_S2)),
1.33/1.55	    inference('simplify', [status(thm)], ['289'])).
1.33/1.55	tff('291', plain, (sk_S1(sk_Xy) | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['290', '247'])).
1.33/1.55	tff('292', plain, sk_S1(sk_Xy), inference('simplify', [status(thm)], ['291'])).
1.33/1.55	tff('293', plain, (sk_S1 = sk_S | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['282', '292'])).
1.33/1.55	tff('294', plain, sk_S1 = sk_S, inference('simplify', [status(thm)], ['293'])).
1.33/1.55	tff('295', plain, ![X1 : a]: sk_S1(X1) = sk_S(X1),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['294'])).
1.33/1.55	tff('296', plain, sk_S(sk_Xz),
1.33/1.55	    inference('demod', [status(thm)], ['249', '295'])).
1.33/1.55	tff('297', plain, (sk_S2(sk_Xx1) = $true | ~ sk_P(sk_S2)),
1.33/1.55	    inference('sup+', [status(thm)], ['0', '90'])).
1.33/1.55	tff('298', plain, (sk_S2(sk_Xx1) = $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['297', '247'])).
1.33/1.55	tff('299', plain, sk_S2(sk_Xx1) = $true,
1.33/1.55	    inference('simplify', [status(thm)], ['298'])).
1.33/1.55	tff('300', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['299', '7'])).
1.33/1.55	tff('301', plain, (~ $true | ~ $true | sk_S2 = sk_Xp(sk_Xx1)),
1.33/1.55	    inference('demod', [status(thm)], ['300', '247'])).
1.33/1.55	tff('302', plain, sk_S2 = sk_Xp(sk_Xx1),
1.33/1.55	    inference('simplify', [status(thm)], ['301'])).
1.33/1.55	tff('303', plain, ![X1 : a]: sk_S2(X1) = sk_Xp(sk_Xx1, X1),
1.33/1.55	    inference('ho_complete_eq', [status(thm)], ['302'])).
1.33/1.55	tff('304', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ sk_P(X5)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X3(sk_Xx2)
1.33/1.55	       | ~ X3(sk_Xx2)),
1.33/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.33/1.55	tff('305', plain,
1.33/1.55	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
1.33/1.55	      (~ X3(sk_Xx2)
1.33/1.55	       | ~ sk_P(X3)
1.33/1.55	       | ~ X4(sk_Xx1)
1.33/1.55	       | ~ X4(sk_Xy1)
1.33/1.55	       | ~ sk_P(X4)
1.33/1.55	       | ~ X5(sk_Xz)
1.33/1.55	       | ~ X5(sk_Xx)
1.33/1.55	       | ~ sk_P(X5)),
1.33/1.55	    inference('simplify', [status(thm)], ['304'])).
1.33/1.55	tff('306', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | ~ sk_P(X1)
1.33/1.55	       | ~ X1(sk_Xy1)
1.33/1.55	       | ~ X1(sk_Xx1)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.33/1.55	    inference('sup-', [status(thm)], ['0', '305'])).
1.33/1.55	tff('307', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a > $o]:
1.33/1.55	      (~ $true
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | ~ sk_P(X1)
1.33/1.55	       | ~ X1(sk_Xy1)
1.33/1.55	       | ~ X1(sk_Xx1)
1.33/1.55	       | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['306', '4'])).
1.33/1.55	tff('308', plain,
1.33/1.55	    ![X0 : a > $o, X1 : a > $o]:
1.33/1.55	      (~ X1(sk_Xx1)
1.33/1.55	       | ~ X1(sk_Xy1)
1.33/1.55	       | ~ sk_P(X1)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['307'])).
1.33/1.55	tff('309', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ sk_S2(sk_Xy1)
1.33/1.55	       | ~ sk_P(X0)
1.33/1.55	       | ~ X0(sk_Xx)
1.33/1.55	       | ~ X0(sk_Xz)
1.33/1.55	       | ~ sk_P(sk_Xp(sk_Xx1))
1.33/1.55	       | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.33/1.55	    inference('sup-', [status(thm)], ['303', '308'])).
1.33/1.55	tff('310', plain,
1.33/1.55	    ![X0 : a > $o]:
1.33/1.55	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)],
1.33/1.55	              ['309', '173', '302', '247', '303', '299'])).
1.33/1.55	tff('311', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.33/1.55	    inference('simplify', [status(thm)], ['310'])).
1.33/1.55	tff('312', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
1.33/1.55	    inference('sup-', [status(thm)], ['296', '311'])).
1.33/1.55	tff('313', plain, (~ $true | ~ $true | ~ $true),
1.33/1.55	    inference('demod', [status(thm)], ['312', '226', '245'])).
1.33/1.55	tff('314', plain, $false, inference('simplify', [status(thm)], ['313'])).
1.33/1.55	
1.33/1.55	% SZS output end Refutation
1.33/1.55	EOF
